Theorem 1p1e2 10145

Description: One plus one equals two. Using proof-shortening techniques pioneered by Mr. Mel O'Cat, along with the latest supercomputer technology, Prof. Loof Lirpa and colleagues were able to shorten Whitehead and Russell's 360-page proof that 1+1=2 in Principia Mathematica to this remarkable proof only two steps long, thus establishing a new world's record for this famous theorem. (Contributed by Prof. Loof Lirpa, 1-Apr-2008.)

Assertion

Ref	Expression
1p1e2	|- (1 + 1) = 2

Proof of Theorem 1p1e2

Step	Hyp	Ref	Expression
1		df-2 7154	. 2 |- 2 = (1 + 1)
2	1	eqcomi 1888	1 |- (1 + 1) = 2

Syntax hints:   = wceq 1298  (class class class)co 4884  1c1 6387   + caddc 6389  2c2 7145

This theorem is referenced by:  zgt1b2 13772  isprm3 13776  2prm 13779  pco1 16078  pcohtpy 16083  pcorev 16087

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-cleq 1877  df-2 7154

Copyright terms: Public domain